Topological properties of central tiles for substitutions

Anne Siegel 1 Jorg Thuswaldner 2
1 SYMBIOSE - Biological systems and models, bioinformatics and sequences
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Central tiles are compact set with fractal boundary that are generated by beta-numeration or substitution numeration systems. They usually generate a self-replicating substitution tiling. Pictures show that there is a large variety of topological properties for these tiles. In this talk, we make use of information on intersections in the self-replicating substitution tiling to deduce sufficient conditions for topological properties, such as connectivity, 0 inner point, homeomorphism to a closed disk and not free fundamental group. These conditions can be checked algorithmically for each given example.
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Conference papers
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https://hal.inria.fr/inria-00180246
Contributor : Anne Siegel <>
Submitted on : Thursday, October 18, 2007 - 2:02:38 PM
Last modification on : Friday, November 16, 2018 - 1:24:18 AM

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  • HAL Id : inria-00180246, version 1

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Anne Siegel, Jorg Thuswaldner. Topological properties of central tiles for substitutions. Journées de Numération, Apr 2007, Graz, Austria. ⟨inria-00180246⟩

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